I have a categorical variable comprising of values from 1 to 7 with these probability:

score   1        2       3      4       5       6   7
p       0.01    0.01    0.03    0.05    0.2   0.3   0.4

In two different samples from the two different populations, I found the same value for 10th percentile (i.e. 4) in observed data. I want to find the likelihood of having exactly the same value for 10th percentile.

FYI, the scores are answers to a scale and probabilities are proportions for each category in a normative sample.I want to be able to do this in R.

P.S.: any suggestion on calculating cumulative distribution of a variable with above-mentioned properties is appreciated.


  • $\begingroup$ Do you mean 'at least 10%', 'at most 10%' or 'exactly 10%'? $\endgroup$
    – Glen_b
    Dec 14, 2013 at 6:29
  • $\begingroup$ @Glen_b I meant exactly 10% but would be happy to learn other possibilities like 'at least 10%' and 'at most 10%'. $\endgroup$
    – Amin
    Dec 14, 2013 at 6:45
  • $\begingroup$ The proportion of times that exactly 1000 observations out of 10000 fall below 4 will be quite small (it's actually possible to compute this number, there's no need to simulate it). $\endgroup$
    – Glen_b
    Dec 14, 2013 at 6:47
  • $\begingroup$ @Glen_b The reason is that in a survey from two different samples from two different populations I found the same value for 10th percentile. I want to know how likely is to find the same value for 10th percentile in a variable.This is why I thought that a simulation would be proper. $\endgroup$
    – Amin
    Dec 14, 2013 at 6:49
  • $\begingroup$ Finding the same value for the 10th percentile is rather different from what you're asking about. $\endgroup$
    – Glen_b
    Dec 14, 2013 at 6:50

1 Answer 1


I think this problem is intractable. This is because you noticed something odd and then want to find how likely it is. But you could have noticed anything else odd that happened. Thus, this is a problem of finding how likely a coincidence is, given that one happened.

However, if you want to pursue this further, Persi Diaconis has done some work on this, e.g. Methods for Studying Coincidences

  • $\begingroup$ It can be seen from this perspective as well. Indeed this coincidence given the fact that the two samples and population are different was surprising for me. $\endgroup$
    – Amin
    Dec 14, 2013 at 14:41
  • $\begingroup$ The link is dead, can you replace it? $\endgroup$ Nov 11, 2022 at 23:25

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